The position vector of 1 kg object is r = (3i - j)m and its velocity v = (3j + k)ms⁻¹. The magnitude of its angular momentum is √(x) Nm where x is ___________. Numerical answer type. Work it out, then open the answer.

Answer: 91. L=m( r× v) with r=(3,-1,0), v=(0,3,1). r× v=[(-1)(1)-0] i-[3(1)-0] j+[3(3)-0] k=- i-3 j+9 k | L|=√(1+9+81)=√(91) So x=91.

The position vector of 1 kg object is r = (3i - j)m and its velocity… | JEE Main 2022 (28 Jun, Shift 1)

Q41JEE Main 2022 · 28 JUN · SHIFT 1Medium

Angular Momentum & its Conservation

The position vector of 1 kg object is $\vec{r} = \left(3\hat{i} - \hat{j}\right)m$ and its velocity $\vec{v} = \left(3\hat{j} + \hat{k}\right)ms^{-1}$ . The magnitude of its angular momentum is $\sqrt{x}$ Nm where x is ___________.

Numerical answer type. Work it out, then open the answer.

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Answer: 91

$\vec L=m(\vec r\times\vec v)$ with $\vec r=(3,-1,0)$ , $\vec v=(0,3,1)$ .
$\vec r\times\vec v=[(-1)(1)-0]\hat i-[3(1)-0]\hat j+[3(3)-0]\hat k=-\hat i-3\hat j+9\hat k$
$|\vec L|=\sqrt{1+9+81}=\sqrt{91}$
So $x=91$ .

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